simpleks (dansig) usuli

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4-mavzu. simpleks (dansig) usuli tayanch so`z va iboralar: simpleks usul, optimallik bahosi, sun`iy o`zgaruvchilar. dars rejasi 1. simpleks jadvalini tuzish. 2. simpleks jadvalida almashtirishlarni bajarish. 3. optimal yechimni aniqlashga doir teoremalar. 4. maqsad funksiyaning chekli minimumga ega bo`lmaslik sharti. 5. simpleks usuli. dansig yaratgan simpleks usul bilan chpm ning optimal yechimini topish uchun chpm kanonik shaklda va cheklamalar sistemasi keltirilgan tenglamalar sistemasi shaklida bo`lishi kerak. simpleks usuli chpm ning optimal yechimini chekli qadamdan so`ng topishga yordam beradi. bizga quyidagi chpm berilgan bo`lsin. (1) (2) (3) ko`rinib turibdiki bu masalada (4.1) cheklamalar keltirilgan tenglamalar sistemasi ko`rinishidadir. (4.1) sistemani vektor shaklida yozib olamiz: , bu yerda vektorlar sistemasi o`lchovli fazoda chiziqli erkli birlik vektorlar sistemasidan iborat bo`lib, bazis vektorlar sistemasini tashkil etadi. ular m o`lchovli fazoning bazisini tashkil qiladi. ushbu vektorlarga mos keluvchi o`zgaruvchilar «bazis (erksiz) o`zgaruvchilar» deb ataladi. o`zgaruvchilar bazis bo`lmagan (erkli) o`zgaruvchilar. agar erkli o`zgaruvchilarga 0 qiymat bersak, bazis o`zgaruvchilar …

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… … … … 0 0 … 0 … … … … … … … … … … … … … … 0 0 … 1 … … (5) formuladan ko`rinib turibdiki, simpleks jadvaldagi bazis vektorlarga mos lar har doim 0 ga teng. agar ustunlarga mos barcha lar uchun shart bajarilsa, u holda yechim optimal yechim bo`ladi. chiziqli funksiyaning minimal qiymati ga teng bo`ladi. shunday qilib, shart (1)-(3) chpm uchun optimallik sharti deyiladi. agar kamida bitta j uchun bo`lsa, u holda masalaning optimal yechimi bo`la olmaydi. bunday holatda topilgan bazis rejani optimal rejaga yaqin bo`lgan boshqa bazis rejaga almashtirish kerak. yangi bazisga kiritiladigan vektorni (6) shart asosida aniqlaymiz. masalan, bo`lsin. demak, yangi bazislar sistemasida vektor bazis vektor sifatida qatnashishi kerak. agar bazisga kiritilsa, u holda eski bazis vektorlardan birortasini bazisdan chiqarish kerak, chunki (1) sistemaga mos matritsaning rangi: . bazisdan chiqariladigan vektorni aniqlash uchun nisbat orqali aniqlovchi koeffitsient tushunchasini kiritamiz. …

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ekshirib boramiz. shunday qilib quyidagi teoremalar o`rinli. 1-teorema. agar biror bir bazis reja uchun tengsizlik o`rinli bo`lsa, u holda bu reja optimal reja bo`ladi. 2- teorema. agar bazis rejada biror bir uchun shart o`rinli bo`lib qolsa, u holda optimal reja bo`lmaydi va uholda shunday rejani topish mumkin bo`ladiki, uning uchun tengsizlik o`rinli bo`ladi. agar biror bir uchun tengsizlik o`rinli bo`lib, bu ustundagi barcha elementlar uchun bo`lsa, u holda masalaning maqsad funksiyasi chekli ekstremumga ega bo`lmaydi. shuning uchun quyidagi shartlarga: 1. ; 2. (1)-(3) masalaning optimal yechimga ega bo`lmaslik sharti deyiladi. agar chpmda maqsad funksiyasi ko`rinishda bo`lsa, u holda masalaning optimallik sharti sifatida: tengsizlikni; masalaning optimal yechimga ega bolmaslik sharti sifatida esa: 1. ; 2. tengsizliklarni qabul qilamiz. misol. quyidagi masalani simpleks usul bilan yeching. yechish. belgilashlar kiritamiz va simpleks jadvalni to`ldiramiz. 0 1 -3 0 2 0 a.k. 0 7 1 3 -1 0 -2 0 - 0 12 0 …

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О "simpleks (dansig) usuli"

4-mavzu. simpleks (dansig) usuli tayanch so`z va iboralar: simpleks usul, optimallik bahosi, sun`iy o`zgaruvchilar. dars rejasi 1. simpleks jadvalini tuzish. 2. simpleks jadvalida almashtirishlarni bajarish. 3. optimal yechimni aniqlashga doir teoremalar. 4. maqsad funksiyaning chekli minimumga ega bo`lmaslik sharti. 5. simpleks usuli. dansig yaratgan simpleks usul bilan chpm ning optimal yechimini topish uchun chpm kanonik shaklda va cheklamalar sistemasi keltirilgan tenglamalar sistemasi shaklida bo`lishi kerak. simpleks usuli chpm ning optimal yechimini chekli qadamdan so`ng topishga yordam beradi. bizga quyidagi chpm berilgan bo`lsin. (1) (2) (3) ko`rinib turibdiki bu masalada (4.1) cheklamalar keltirilgan tenglamalar sistemasi ko`rinishidadir. (4.1) sistemani vektor shaklida yozib ola...

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